Structural
Column Buckling Calculator (Euler and AISC)
Slender columns fail by buckling before they crush. This calculator finds the Euler elastic buckling load and, for steel, the AISC 360 critical stress and design strength φPn. For estimation only; a licensed PE must design.
Formula
Euler: Pcr = π²EI/(KL)², with KL in inches. Fe = Pcr/A = π²E/(KL/r)², r = √(I/A). AISC 360-22 Section E3: if Fy/Fe ≤ 2.25, Fcr = 0.658^(Fy/Fe) × Fy (inelastic); otherwise Fcr = 0.877Fe (elastic). Design strength φPn = 0.90 × Fcr × A.
Worked example
W8x31 (A = 9.13 in², Iy = 37.1 in⁴), pinned both ends (K = 1.0), 12 ft long, Fy = 50 ksi: Pcr = π² × 29,000 × 37.1 ÷ 144² = 512.1 kips. r = 2.02 in, KL/r = 71.4. Fe = 56.1 ksi. Fy/Fe = 0.89 ≤ 2.25, so Fcr = 0.658^0.89 × 50 = 34.4 ksi and φPn = 0.9 × 34.4 × 9.13 = 282.9 kips, consistent with AISC Manual column tables.
Assumptions and limits
- Concentrically loaded, initially straight, prismatic member.
- Uses the weak axis unless bracing differs by axis; check both axes.
- Does not check local buckling of slender elements, torsional buckling, or combined axial and bending.
- Euler applies to any linear elastic material; the AISC equations apply only to steel.
- For estimation only. A licensed Professional Engineer (PE) must design and stamp any structural, foundation or life-safety element.
Frequently asked questions
What K factor should I use?
Theoretical K is 1.0 for pinned-pinned, 0.5 for fixed-fixed, 0.7 for fixed-pinned and 2.0 for a cantilever (fixed-free). AISC Commentary Table C-A-7.1 gives recommended design values that are slightly higher for imperfect fixity.
Why is the AISC strength lower than the Euler load?
Real columns have residual stresses and initial crookedness, and stocky columns yield before reaching the Euler load. The AISC curve accounts for both.
What is a slender column?
One whose KL/r is high enough that buckling controls. In AISC terms, elastic buckling governs when Fy/Fe exceeds 2.25, about KL/r of 113 for 50 ksi steel. AISC recommends KL/r not exceed 200.